Bounds and Maxima for the Workload in a Multiclass Orbit Queue-Reference-Cited by-同舟云学术

Bounds and Maxima for the Workload in a Multiclass Orbit Queue

Published:2023-01-20 Issue:3 Volume:11 Page:564
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Morozov Evsey V.¹²³^ORCID,Peshkova Irina V.¹²^ORCID,Rumyantsev Alexander S.¹²^ORCID

Affiliation:

1. Department of Applied Mathematics and Cybernetics, Petrozavodsk State University, 185910 Petrozavodsk, Russia

2. Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia

3. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia

Abstract

In this research, a single-server M-class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical M/G/1 systems where the service time has M-component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes.

Funder

Russian Science Foundation

Ministry of Education and Science Russia

Publisher

MDPI AG

Subject

General Medicine

Link

https://www.mdpi.com/2227-7390/11/3/564/pdf

Reference40 articles.

1. Accessible bibliography on retrial queues;Artalejo;Math. Comput. Model.,1999

2. Artalejo, J., and Gomez-Corral, A. (2008). Retrial Queueing Systems: A Computational Approach, Springer.

3. Fayolle, G. A Simple Telephone Exchange with Delayed Feedbacks. Proceedings of the International Seminar on Teletraffic Analysis and Computer Performance Evaluation.

4. Retrial queues with collision arising from unslotted CSMA/CD protocol;Choi;Queueing Syst.,1992

5. The M/G/1 retrial queue with retrial rate control policy;Choi;Probab. Eng. Inf. Sci.,1993